Two-tier networks comprise a conventional cellular network overlaid with shorter range second-tier networks or hotspots, also referred to as small-cells, such as using femto-cells, distributed antennas, or relays. Such coexisting systems can increase spectral efficiency for serving users. Some second-tier systems have priorities and can allow some level of interference to the primary systems, e.g. conventional cellular networks or macro-cells. Other second-tier systems can opportunistically transmit without interfering with existing primary systems. Such opportunistic two-tier systems include the so-called Vandermonde frequency Division Multiple Access (VFDM) systems which allow the coexistence of a macro-cell comprising multiple primary users and a small-cell comprising multiple secondary user pairs. In VFDM, precoding at small-cell transmitters causes no interference to the macro-cell. However, a drawback of such systems is that precoding at the small-cell transmitters is carried out independently, thereby causing a waste of extra transmit dimensions as well as low efficiency linear precoding due to dimension restriction. An improved precoding scheme for two-tier cellular networks is needed.